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Abstract

In this paper pencils of partial differential operators depending polynomially on a
complex parameter and corresponding boundary value problems with general boundary
conditions are studied. We define a concept of ellipticity for such problems (for which
the parameter-dependent symbol in general is not quasi-homogeneous) in terms of the Newton
polygon and introduce related parameter-dependent norms. It is shown that this type of
ellipticity leads to unique solvability of the boundary value problem and to two-sided a
priori estimates for the solution.